confused about vega

[financeguy]

alright I get it, thanks for the explanation. I admit that I'm a bit shocked that summing the total vega is widely used, when at the same time the skew is also widely used, and that I see nowhere the mention that these 2 are incomptatible (or least, I never see the mention that a no-skew assumption is made when summing the vegas)

So like I said in the previous post, you look at the vega in conjunction with your smile risk. Your smile risk is important too, but vega is a first order problem and smile risk is second. This is why traders are concerned with vega before considering smile risk. There are ways to try to approximate your total volatility smile risk from ATM implied volatility going up or down 1 vol. Vega, as we're discussing it, holds risk reversals and butterflies constant and bumps the whole smile in parallel. Technically speaking this should be done in delta space rather than in strike specific space, so if we're looking at a specific OTM strike, this will shift by a slightly different amount from the ATM volatility, as it is no longer the same delta as it was before. In any case, as you rightly point out, whatever the perturbation in the smile the vega number captures does not tell the whole story of our risk. It might stand to reason, for instance, that if some event occurs that moves ATM volatility higher, OTM options should increase even more than the ATM point as fat tails become more likely than they were before. One thing you can do to adjust for this is to bump your smile greeks such that the parameters of your smile model remain constant. For example, in a SABR model, if you bump your ATM vol higher but leave your butterflies constant, your implied vol of vol will be lower than it was before as the wingyness on a vol adjusted basis has become smaller. To account for this, we might calculate a risk number that, in addition to the vol bump, also bumps the butterflies in order to preserve the value of the implied vol of vol within the model. The same could be done simultaneously for the underlying vs implied vol correlation parameter. The resulting pnl shock number would in theory be more reflective of the risk you run if ATM implied vol were to move meaningfully, as it captures the larger move in OTM options. You could also simply make a judgement call as to where you think the volatilities of OTM options will go if ATM volatility moves a given amount. I do want to stress, however, from a practical point of view, if today you were given a portfolio to hedge consisting of a bunch of delta hedged options, the first thing you would do is buy or sell ATM options to hedge your vega - which would eliminate the vast majority of your market risk - and then over time work out of your smile risk which moves a lot more slowly.

 

[A modest quant]

Hi intelligent ppl,

Please kindly help me to understand implied vol. If one doesnot invert option prices thru BS formula (a wrong formula for pricing derivatives), i.e. one views risk directly thru prices, how does one know what sort of risk(s) he is dealing with? Thanks in advance.

 

[financeguy]

If you don't want to adhere to market convention, then I suppose you can create whatever (within reason) model you want and have risks in terms of sensitivities to inputs of that model. I would urge you to reconsider writing off market convention, however, as the implied volatility smile created by inverting the black-scholes formula across strikes contains a wealth of information about the market's implied distribution of asset returns, the underlying's position at expiry, correlation of the vol and underlying, and the vol of vol - and therefore risks consistent with these concepts as implied by the market, which are by definition directly hedgeable in the market.

 

[A modest quant]

If you don't want to adhere to market convention, then I suppose you can create whatever (within reason) model you want and have risks in terms of sensitivities to inputs of that model. I would urge you to reconsider writing off market convention, however, as the implied volatility smile created by inverting the black-scholes formula across strikes contains a wealth of information about the market's implied distribution of asset returns, the underlying's position at expiry, correlation of the vol and underlying, and the vol of vol - and therefore risks consistent with these concepts as implied by the market, which are by definition directly hedgeable in the market.

As traders, i among other traders make market conventions by which we communicate and maket trades. By no means, market conventions encompass all relevant aspects of risks involving in our trades or prices we make. As a trader, i make prices and trade, and therefore i make market. In other words, i am the market and i am your implied information. What information can you imply from prices that i myself make?

You viewed risks as if they are simply just derivatives of a mathematical function with respect to its variables. Your view on risks is quite disturbing!

I am a trader, i use conventions and intuition, not definitions, to make prices. You used definitions, vol of vol, etc... and tried to explain prices. Your explanation is quite absurd!

 

[financeguy]

What's your angle here? What point are you trying to get across with these posts?

 

[A modest quant]

What's your angle here? What point are you trying to get across with these posts?

What's my angle? In my posts, I hope to receive good discussions from people who are out there in the real world, giving me realistic insights, no-nonsense stuffs that are beyond conventions and textbook models, assumptions, definitions. Especially, i don't want to listen to what i've already known.

 

[ripintheblue]

I'm an options trader. Here's what we do. We look at the sum of vega (technically smile vega, not B-S vega, but assume B-S vega for these purposes) of all our options. We generally bucket by tenor, like 1M, 3M, 6M, 1Y, etc, as each point in the term structure doesn't always move in parallel. But again, we're talking about vol vs skew risk so let's just assume the curve does move in parallel for this exercise. Then when the implied vol of the ATM's go up or down, we expect our pnl from that happening to be our portfolio's vega times the move in the implied vol of the at-the-moneys. Now we also have sensitivity to how the smile moves. For that we have greeks defined as sensitivities to generic risk reversals and butterflies traded in the market, different places call them different things. So if, in addition to the implied vols of ATM options causing vega pnl we have the implied vols of risk reversals and butterflies moving, that will cause additional pnl for the out-of-the-money options in our book. We generally mark to generic % OTM risk reversal / fly or % delta risk reversal / fly, and then re-interpolate our smile and find what our change in implied vols were to each option in our book. In any case, any OTM option will have some vega, some sensitivity to risk reversal, and some sensitivity to butterfly prices. Then our expected pnl is the sum product of the three risks times changes in each smile parameter (atm vol, risk reversal, butterfly).

Also, generally speaking, vega is a good first order approximation of your risk, because if the ATM options go up in vol, it's very unlikely that the vols of any OTM options vols go down (and vice versa). So it's not totally silly to try to manage the sum of your portfolio's vega.

Hope that helps.

why do you calculate ATM opt & butterfly & risk reversal vega? don't they move parallel?